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https://github.com/kalmarek/SmallHyperbolic
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finally correct eigenvalues!
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29244c5480
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90
PSL.jl
90
PSL.jl
@ -1,5 +1,6 @@
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using Nemo
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using DelimitedFiles
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using LinearAlgebra
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include("src/nemo_utils.jl")
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@ -7,7 +8,7 @@ const PRECISION = 256
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function parse_eval(expr_str, value, var_name)
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ex = Meta.parse(expr_str)
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svar = :($var_name)
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svar = :($var_name)
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return @eval begin
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let $svar = $value
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$ex
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@ -16,9 +17,9 @@ function parse_eval(expr_str, value, var_name)
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end
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function read_eval(fname, var_name, value)
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a = readdlm(fname, ',', String)
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a .= replace.(a, '/'=>"//")
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return parse_eval.(a, value, var_name)
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a = readdlm(fname, ',', String)
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a .= replace.(a, '/' => "//")
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return parse_eval.(a, value, var_name)
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end
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function load_discrete_repr(i, q = 109; CC = AcbField(PRECISION))
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@ -27,13 +28,19 @@ function load_discrete_repr(i, q = 109; CC = AcbField(PRECISION))
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ra = read_eval(
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"data/Discrete reps PSL(2, $q)/discrete_rep_$(i)_a.txt",
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:Z, ζ)
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:Z,
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ζ,
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)
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a = matrix(CC, [CC(s) for s in ra[1:degree, 1:degree]])
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rb = read_eval(
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"data/Discrete reps PSL(2, $q)/discrete_rep_$(i)_b.txt",
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:Z, ζ)
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:Z,
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ζ,
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)
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b = matrix(CC, [CC(s) for s in rb[1:degree, 1:degree]])
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@assert contains(det(a), 1)
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@assert contains(det(b), 1)
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return a, b
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end
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@ -44,46 +51,61 @@ function load_principal_repr(i, q = 109; CC = AcbField(PRECISION))
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ra = read_eval(
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"data/Principal reps PSL(2, $q)/principal_rep_$(i)_a.txt",
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:zz, ζ)
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:zz,
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ζ,
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)
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a = matrix(CC, [CC(z) for z in ra[1:degree, 1:degree]])
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rb = read_eval(
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"data/Principal reps PSL(2, $q)/principal_rep_$(i)_b.txt",
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:zz, ζ)
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:zz,
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ζ,
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)
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b = matrix(CC, [CC(z) for z in rb[1:degree, 1:degree]])
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@assert contains(det(a), 1)
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@assert contains(det(b), 1)
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return a, b
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end
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function safe_eigvals(m::acb_mat)
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evs = eigvals(m)
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all(isfinite.(evs)) && return evs
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CC = base_ring(m)
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X = matrix(CC, rand(CC, size(m)))
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return eigvals(X * m * inv(X))
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evs = eigvals(X * m * inv(X))
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all(isfinite.(evs)) && return evs
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throw(ArgumentError("Could not compute eigenvalues"))
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end
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for i in 0:27
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try
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a,b = load_principal_repr(i)
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adjacency = sum([[a^i for i in 1:4]; [b^i for i in 1:4]])
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@time evc = safe_eigvals(adjacency)
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ev = sort(real.(first.(evc)), lt=<, rev=true)
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@info "Principal Series Representation $i" ev[1:2]
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catch ex
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@error "Principal Series Representation $i failed"
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ex isa InterruptException && throw(ex)
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end
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end
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if !isinteractive()
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for i = 0:27
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try
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a, b = load_principal_repr(i)
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adjacency = sum(a^i for i = 1:4) + sum(b^i for i = 1:4)
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@time ev = let evs = safe_eigvals(adjacency)
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_count_multiplicites(evs)
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end
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for i in 1:27
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try
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a,b = load_discrete_repr(i)
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adjacency = sum([[a^i for i in 1:4]; [b^i for i in 1:4]])
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@time evc = eigvals(adjacency)
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ev = sort(real.(first.(evc)), lt=<, rev=true)
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@info "Discrete Series Representation $i" ev[1:2]
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catch ex
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@error "Discrete Series Representation $i : failed"
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ex isa InterruptException && rethrow(ex)
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end
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@info "Principal Series Representation $i" ev[1:2] ev[end]
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catch ex
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@error "Principal Series Representation $i failed" ex
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ex isa InterruptException && throw(ex)
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end
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end
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for i = 1:27
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try
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a, b = load_discrete_repr(i)
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adjacency = sum(a^i for i = 1:4) + sum(b^i for i = 1:4)
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@time ev = let evs = safe_eigvals(adjacency)
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_count_multiplicites(evs)
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end
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@info "Discrete Series Representation $i" ev[1:2] ev[end]
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catch ex
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@error "Discrete Series Representation $i : failed" ex
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ex isa InterruptException && rethrow(ex)
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end
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end
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end
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@ -1,3 +1,5 @@
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Base.hash(a::acb, h::UInt) = h
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import Base.reim
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reim(x::Nemo.acb) = reim(convert(ComplexF64, x))
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@ -153,5 +155,5 @@ function _count_multiplicites(evs)
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push!(λ_m, (evs[i], m))
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i += m
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end
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return λ_m
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return sort(λ_m, lt=(a,b)->(real(first(a))<real(first(b))), rev=true)
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end
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